Find slopes and point of 1. y—4=2(x-3) 2. y—3=-6(x—2) 3. y+11=3(x—2) 4. y+14 =1/2(x+19) answer these

Question part points submissions used suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a party. of these 100 tickets, only 12 are winning tickets. the generalized pigeonhole principle guarantees that there must be a streak of at least l losing tickets in a row. find l.

Simplify (2^5/3^2)^4 a. 2^20/3^8 b. 2^9/3^8 c. 8^5/12^2 d. 2/3^2

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)